Theorems · Theorem · category theory
CategoryTheory.Adjunction.faithful_R_of_epi_counit_app
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{L : CategoryTheory.Functor C D} {R : CategoryTheory.Functor D C} (h : L ⊣ R)
[∀ (X : D), CategoryTheory.Epi (h.counit.app X)], R.FaithfulIf each component of the counit is an epimorphism, then the right adjoint is faithful.
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- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
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